Electrically-variable transmissions typically have an input member connected to an engine and one or two motor/generators connected to different members of planetary gear sets to allow one or more electrically-variable modes of operation, fixed speed ratio modes, and an electric-only (battery powered) mode, when connected with a battery. Electrically-variable transmissions may improve vehicle fuel economy in a variety of ways. For instance, the engine may be turned off at idle, during periods of deceleration and braking, and during periods of low speed or light load operation to eliminate efficiency losses due to engine drag. Captured braking energy (via regenerative braking) or energy stored by one of the motors acting as a generator during periods when the engine is operating is utilized during these engine off periods to keep the engine off longer, supplement engine torque or power and/or operate at a lower engine speed, or supplement accessory power supplies. Transient demand for engine torque or power is supplemented by the motor/generators during operation in engine-on, electrically-variable modes, allowing for downsizing the engine without reducing apparent vehicle performance. Additionally, the engine may be operated at or near the optimal efficiency point for a given power demand because the speed ratio between the engine and the output member of the transmission can be continuously variable by the action of a gear set and a motor/generator. Additionally, the motor/generators are very efficient in accessory power generation and electric power from the battery serves as an available torque reserve allowing operation at a relatively low transmission numerical speed ratio.